Final answer:
The rise in water level is determined by calculating the volume of the submerged solid and the surface area of the cylindrical container's base. Using the dimensions provided for the solid and the cylinder's diameter, we apply Archimedes' principle to find the rise.
Step-by-step explanation:
The question asks about the rise in water level when a solid object is submerged in a cylindrical container, which involves the use of Archimedes' principle. To find the rise in the water level, we must calculate the volume of the solid object and then determine how that volume will affect the water level in the cylindrical container.
The volume of the rectangular solid (iron) is calculated using the formula for the volume of a rectangular prism: Volume = length × width × height. Therefore, the volume for the given solid is 32 cm × 22 cm × 14 cm which equals 9856 cm3.
To find the rise in water level, we divide this volume by the base area of the cylindrical container. The area of the base of the cylinder (which is a circle) is given by Area = π × radius2. The diameter is given as 56 cm, so the radius is 28 cm. The area of the base is π × (28 cm)2.
Finally, the rise (ΔH) in water level is calculated by the formula ΔH = Volume of solid / Area of base of cylinder. Substituting the known values, the rise in water level can be found. It is important to work with consistent units and convert the rise into meters or centimeters as required.